If you're not leaning forward, are you putting your weight into the punch? Is it a strong punch? In a strong punch, even if I don't set out to lean forward, the motion of my arm pulls my upper body forward. It's certainly possible to punch without shifting your whole weight into it (boxers do it all the time), but it's a weaker punch and doesn't read as clearly. When animating, it's usually best to exaggerate these things.
As for hovering and punching - you've probably heard the law "for every force there is an equal and opposite force." When we stand on the ground, the ground pushes back at us. When we direct energy forward, like in a punch, the rest of the body moves backwards, but the ground stops it, and reflects that energy back into us. When the punch connects, the fact that we're on the ground is the reason we don't fall backwards (from the opposing force of the object we're hitting). In fact, this can happen even when there is the ground, if your feet aren't positioned in a way to redirect that force into the ground - poor footing can throw you off-balance because it doesn't brace you against the ground.
In space (or suspended underwater or in midair), there is no ground. Inertia keeps things where they are, but if a part of that object moves in one direction, then the rest of it will move in the other direction (the distances depend on the masses of the different parts). A punch that doesn't connect will necessarily direct parts of the body backwards, though the center of mass will remain where it was. A punch that does connect will send the puncher and the punchee in opposite directions unless the punchee is braced (if they are, then the puncher will be sent flying backwards! Probably not what the puncher intended!).
In other words, if characters aren't braced against the ground, you'll probably want to show where they're getting the force that keeps them moving forward, such as rocket boosters on their backs. The positions of these boosters might in turn influence the kinds of attacks the characters can make. For example, if their boosters are on their back, then they can only send them moving forward. If they try to do a punch that twists their body to the side (like most punches done by humans), then they'll no longer be facing the way they want to face! If you put rocket boosters on their arms and they punch in a rotating motion, then you'll likely want the booster on the non-punching arm going during the punch, to counteract the rotation produced by the punching arm.
If you want a demonstration of these principles in action, try finding a rolling chair that rolls easily, and a smooth floor. The easier it is to set that chair rolling, the better it'll approximate "space". Sit on it with your feet off the ground, and punch the air with all your strength. You'll most likely notice the chair move slightly backwards! Mine has pretty bad wheels, but even so it moves back several centimetres with every punch, and I'm weak! I could probably roll myself all the way to the kitchen if I punch enough :] If you punch a wall with a lot of strength (make sure you wear gloves and that it's a solid wall that won't break, and have plenty of space behind you!), you'll roll backwards quite a bit!